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A company makes plastic beach balls with a radius of 2 inches. How many square inches of plastic does the company need to make 10 beach balls? Use 3.14 for [tex]\pi[/tex] and round to the nearest tenth.

Recall the formula [tex]SA = 4\pi r^2[/tex].

A. 50.24 in.[tex]^2[/tex]
B. 100.5 in.[tex]^2[/tex]
C. 251.2 in.[tex]^2[/tex]
D. 502.4 in.[tex]^2[/tex]

Answer :

To solve the problem, we start by finding the surface area of one beach ball. The formula for the surface area of a sphere is given by

$$
SA = 4 \pi r^2.
$$

Here, the radius is $r = 2$ inches and we use $\pi = 3.14$. Substituting these values into the formula, we have

$$
SA = 4 \times 3.14 \times (2)^2.
$$

Since $(2)^2 = 4$, the calculation becomes

$$
SA = 4 \times 3.14 \times 4 = 50.24 \text{ square inches}.
$$

This is the surface area required for one beach ball.

Next, since the company makes $10$ beach balls, the total surface area needed is

$$
\text{Total Surface Area} = 10 \times 50.24 = 502.4 \text{ square inches}.
$$

Thus, the company needs $502.4$ square inches of plastic to make $10$ beach balls.

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Rewritten by : Barada